Problem: Simplify the following expression: $\dfrac{40q^5}{5q^4}$ You can assume $q \neq 0$.
$ \dfrac{40q^5}{5q^4} = \dfrac{40}{5} \cdot \dfrac{q^5}{q^4} $ To simplify $\frac{40}{5}$ , find the greatest common factor (GCD) of $40$ and $5$ $40 = 2 \cdot 2 \cdot 2 \cdot 5$ $5 = 5$ $ \mbox{GCD}(40, 5) = 5 $ $ \dfrac{40}{5} \cdot \dfrac{q^5}{q^4} = \dfrac{5 \cdot 8}{5 \cdot 1} \cdot \dfrac{q^5}{q^4} $ $\phantom{ \dfrac{40}{5} \cdot \dfrac{5}{4}} = 8 \cdot \dfrac{q^5}{q^4} $ $ \dfrac{q^5}{q^4} = \dfrac{q \cdot q \cdot q \cdot q \cdot q}{q \cdot q \cdot q \cdot q} = q $ $ 8 \cdot q = 8q $